Is it possible to add fake user to animation actions after saving model without having done so?
Yes, you can still bring this back as long as you haven't closed Blender. If you did close Blender, you can only bring it back if there was an item that's using the datablock containing that Action. The whole reason for giving a datablock a fake user is to stop Blender from cleaning it out along will all the other un-needed items when you close it. I suspect it to be a resource thing.

In the Dope Sheet window, switch the mode from 'Dope Sheet' over to 'Action Editor'. There should be a dropdown next to the Key menu option at the bottom of the Dope Sheet Window that lets you do this.

Further down the menus at the bottom of the Dope Sheet Window, there should be an Action Selector. The look of this selector changes a bit based on whether or not an Action is currently selected. Either way, there will be a dropdown button with an image of three diamonds forming an upside-down triangle. If no action is currently selected, there will be a button that lets you create a new action. If an action is selected, there will be a text box with the Action's name, followed by the fake user button, create new action (based on current action) button, and de-select action (un-link datablock) button. Use that drop-down to select the Action you want to add a fake user to.

Once the Action is selected, you can add (or remove) the fake user.